Recorded line profiles in pure H 2 , Ar and 2.7% H 2 mixture, and He 

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... ions reach the cathode where they neutralize or neutralize and fragmentize. The back-reflected particles from the cathode are H f atoms directed back to the discharge. 1,2 After collisions of H f with H 2 and/or with other discharge constituents, H f * is produced. Experimentally fast excited hydrogen atoms moving in both directions towards and from the cathode are detected in different discharges in pure hydrogen and in hydrogen mixtures with inert gases by means of Doppler spectroscopy of Balmer lines. 1–5 Depending upon discharge conditions, the excited hydrogen atoms with ener- gies ranging from several tens up to several hundreds of eV are detected. In a hydrogen–argon mixture, as a consequence of the dominant concentration of H 3 ϩ ions, Balmer line profiles are narrower ͑ lower average Doppler temperature ͒ , which is expected for the heavy three-atomic molecular ions. 2,3 Therefore, up to this point, all explanations of excessive Balmer line broadening in low pressure gas discharges with hydrogen are based on a gain of ion energy in an electric field and collisional generation of fast excited hydrogen atoms. Mills et al. 6,7 offered another explanation for excessive Balmer line broadening, which is based on resonant energy transfer. According to the authors, large Doppler line broadening appears only when plasma is formed by a resonance transfer mechanism involving the species providing a net enthalpy of a multiple of 27.2 eV and atomic hydrogen. Since Ar ϩ , He ϩ , and strontium each ionize at an integer multiple of the potential energy of atomic hydrogen, a dis- charge in a mixture of one or more of these species with hydrogen forms a resonance transfer ͑ RT ͒ plasma. In order to confirm the theory of RT plasma formation, the authors 6,7 used ͑ a ͒ numerous arguments based on elementary collision processes in gas discharges and ͑ b ͒ offered the results of an experimental study of excessive H ␣ and in some cases L ␣ line broadening in GD and MID. As already pointed out, the results in GD and MID ͑ see Ref. 6, Tables I and II ͒ show excessive H ␣ Doppler broadening in Ar/H 2 , He/H 2 , and Sr/H 2 , which is in agreement with their expectation. So far, the effect of excessive line broadening has been reported in dc glow and radio-frequency discharges, but not in MID. An extensive case history exists on the excessive Balmer line broadening in a variety of discharges. 1–5 These results, together with the studies of excessive Balmer line broadening, started in pure hydrogen 8,9 and the earlier reported results 10,11 of excessive Balmer lines broadening studies in Ne/H 2 , Kr/H 2 , and Xe/H 2 mixtures contradict the data presented in Ref. 6. Mills et al. 7 proposed a different mechanism of line broadening and use their experimental results 6 as possible evidence of validity of their resonant transfer plasma theory. According to Mills et al. 6,7 the key arguments in favor of RT plasma formation are results for excessive H ␣ broadening detected in microwave discharge ͑ see Ref. 6, Table II ͒ . In contrast to glow discharges a strong electric field does not exist in MID, and thus hydrogen ions cannot gain energy required for collisional excitation of H f * . For further confir- mation of RT plasma formation, in addition to the data in Table II ͑ Ref. 6 ͒ , the authors use an example of the L ␣ line profile recorded in MID with a full half width of 10 nm. Experimental results reported by Mills et al. 6 open at least two additional questions: ͑ 1 ͒ What is the parameter range where the excessive Balmer line broadening can be observed in MID? ͑ 2 ͒ What is the mechanism of generation of fast hydrogen atoms in MID and are there conditions in MID favorable for generation of a certain number density of fast excited hydrogen atoms, similar to those identified in dc glow or RF discharges, leading to the excessive Balmer line broadening? The goal of present work is to address these questions and elucidate the mechanisms of Balmer line broadening in MID. In order to test the presence of excessive hydrogen Balmer line broadening in MID two experiments were performed and the results of the line shape studies in pure hydrogen and in Ar/H 2 and He/H 2 gas mixtures are presented. For these experiments microwave discharges are induced within the rectangular Evenson’s 12 and coaxial Beenaker’s 13 cavity. In this work we were focused only on the hydrogen Balmer lines, but an additional concern can be raised for the resonant Lyman alpha line in microwave discharges. Lyman alpha is almost always optically thick, usually indicated with a flattened peak and a broadened shape. Gas mixtures in microwave discharges at low pressures are far from equilib- rium, and exact calculation of the Lyman-alpha profile is rather elaborate. However, the simplified analysis presented below indicates an excessive ‘‘effective path length’’ for the case of the vacuum–ultraviolet radiation spectrum from the microwave discharge described in Fig. 5 of Ref. 6. The trans- lational temperature of heavy particles in microwave discharges is, typically, between 500 and 1500 K. The oscillator strength of the Lyman-alpha transition 14 is 0.416. Therefore, its absorption cross section 15 has the value of ␴ 0 ϭ (1.4– 2.4) ϫ 10 Ϫ 13 cm Ϫ 3 . The total number density of hydrogen at 300 mTorr in the temperature range 500–1500 K, in a 97/3% mixture 6 of Ar/H 2 is between 6 ϫ 10 14 and 1.8 ϫ 10 15 cm Ϫ 3 . Based on the electron impact dissociation rate 16 of 2 ϫ 10 Ϫ 9 cm 3 s Ϫ 1 , and a typical electron number density of 10 12 cm Ϫ 3 , we estimate the number density of atomic hydrogen at N ϭ (3 – 9) ϫ 10 13 cm Ϫ 3 . Using the above absorption cross section, the number density of the atomic hydrogen, and the discharge length of l ϭ 5 cm, we evaluated the effective path length for the Lyman-alpha absorption in the excited Ar/H 2 mixture to be N ␴ 0 l ϭ (20– 220). Therefore, in the typical range of parameters in a microwave discharge at low pressures, the Lyman-alpha line is optically thick and it is not possible to make a clear conclusion based on its observed profile. A schematic diagram of the experimental setup is given in Fig. 1 ͑ a ͒ . A microwave discharge was sustained with an appliance-type magnetron-driven microwave generator at 2.45 GHz coupled to an Evenson’s cavity designed to sup- port the TE 111 mode. The discharge is generated in a se- quence of microwave pulses of duration between 3 and 6 ms with a repetition rate of 60 pps. The radius of the cylindrical cavity was R ϭ 3.83 cm. The length of the cavity was set to two microwave wavelengths, L ϭ 24.5 cm. A sealed-off quartz tube with 33 mm O.D. and 30 mm I.D. was positioned along the axis of the cavity. At prebreakdown conditions, the electric field in the central section of the discharge was rectangular to the axis of the tube. Discharge was initiated and sustained at magnetron power between 0.75 and 1 kW in a train of pulses with duration 3– 6 ms, depending on the power. A calibrated mixture of 95% argon and 5% hydrogen with a small addition of nitrogen was flown through the tube at a constant pressure in the range between 0.5 and 100 mbar. A 5 ϫ 2.5 mm 2 slit section from the center of the discharge was imaged with a quartz telecentric lens system to the entrance slit of a 0.5 m imaging spectrometer ͑ Acton ͒ with a coated 1800 g/mm grating, blazed at 500 nm. The possible effects of the second-order spectrum were elimi- nated with a glass filter in front of the entrance slit. The detection system consisted of an Acton imaging spectrometer with an Apogee camera and a Hamamatsu charge-coupled- device detector (1024 ϫ 256 pixels). The pixel size of the detector was about 25 ␮ m. The instrumental full width at half maximum ͑ FWHM ͒ was measured to be 0.022 03 nm for 486.133 nm, and 0.0195 nm for 656.28 nm. Every individual spectrum was obtained by integrating about 2000 discharge pulses. The radial distribution of line radiation obtained with the imaging spectrometer has shown no visible change in hydrogen line intensities, line profiles, and wing behavior. This is consistent with electric field cal- culations for the central cross section of the TE 111 cavity, which show that the electric field is practically constant and perpendicular to the axis of the tube. A schematic diagram of the experimental setup is presented in Fig. 1 ͑ b ͒ . As a power supply, a commercial 2450 MHz generator connected by a waveguide to the TEM 010 -type Van Dalen’s modification 17 of Beenakker microwave cavity 13 is used. An 18-cm-long quartz tube with 3.5 mm I.D. is installed in the center of microwave cavity. All measurements are performed with microwave power between 40 and 80 W. For 80 W power input, the reflected power did not exceed 5 W in hydrogen and was less than 1 W in other cases. Gas flow of hydrogen ͑ purity 99.995% ͒ and argon and helium gas mixtures was sustained at a se- lected pressure ranging between 0.5 and 10 mbar by means of a needle valve and a two-stage mechanical vacuum pump. Experimental conditions microwave power input and gas pressure ͒ are kept as close as possible to the conditions in Ref. 6. The plasma source is imaged 1:1 onto the entrance slit of a 0.5 m Ebert-type spectrometer with inverse dispersion 1.6 nm/mm. Spectra intensities are recorded by means of a pho- tomultiplier mounted at the exit slit of the spectrometer. Ro- tating the spectrometer grating with a stepping motor con- trolled with a PC performs the wavelength scanning. The emission spectra were recorded with a boxcar averager and the same computer. Consider a mixture of two groups of hydrogen atoms, with densities N 1 and N 2 , at temperatures T 1 and T 2 . Total intensity profiles of lines emitted by the mixture due to Doppler broadening will be given ...

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... the Doppler width corresponding to the most probable velocity in the velocity distribution of the species i assuming, for simplicity, a Maxwellian velocity distribution of both groups of hydrogen atoms. The total emission intensity of the H ␤ line for mixtures of fast ( T 1 ϭ 4 ϫ 27.2 eV ϭ 108.8 eV) and slow ( T 2 ϭ 0.1 eV) hydrogen emitters is given in Fig. 2. The mixtures contain 99.9%, 95%, and 5% fast hydrogen atoms, respectively. Superposition of these two groups of hydrogen atoms should produce a Doppler line profile with a FWHM of about 0.2 nm, and a more or less pronounced, second profile with a FWHM of about 0.006 nm. The relative concentration of fast atoms has to be extremely high in order to practically eliminate the effect of the slow atoms on the line profile. However, the effect of the fast atoms is almost invisible already at a relative concentration of 5%. We recorded hydrogen line spectra over a pressure range between 0.3 and 100 mbars and were not able to observe any excessive broadening of the H ␣ and H ␤ line profiles, with a FWHM ranging from 0.04 to 0.05 nm, depending on pressure and power density ͓ see Figs. 3 ͑ a ͒ –3 ͑ c ͔͒ . In a series of separate measurements, we measured rotational temperatures of hydrogen and nitrogen molecules. All rotational temperatures fall in the range between 950 and 1150 K. Therefore, we have good reason to assume that the hydrogen atom temperature is not higher than 1050 K, and that the Doppler FWHM is about 0.0057 nm. This value is about four times smaller than the instrumental profile, and about 6 – 8 times smaller than the measured profiles. As shown in Figs. 3 ͑ a ͒ –3 ͑ c ͒ , we could not find any evidence of fast hydrogen atoms in the microwave cavity discharge with rectangular electric field. The quantitative modification of atomic hydrogen Balmer line profiles, H ␣ and H ␤ , due to the presence of fast hydrogen atoms, is of the order of 0.001 in comparison to thermal atoms. Therefore, the relative presence of fast hydrogen atoms with kinetic energy several tens eV or higher should be on the level 0.01% or lower. The measured linewidths of H ␣ and H ␤ are 2–2.5 times larger than the instrumental half widths. Therefore, they are based on an underlying broadening mechanism. If the broadening is based on the Doppler effect only, the temperature of hydrogen would be higher, but comparable to the electron temperature in the discharge. This could lead to the conclusion that fast atoms were generated by a charge-transfer mechanism from the ions accelerated in the electric field ͓ see reactions ͑ 1 ͒ – ͑ 3 ͔͒ . Since the electric field in the cavity is polarized, the effect should not be isotropic. We performed a series of separate tests at two mutually perpendicular lines of observation and did not see any change in the line profiles. Therefore, we concluded that the effect of charge transfer is negligible. The only remaining mechanism capable of modifying the line profile on the measured scale is Stark broadening. After deconvolution of the instrumental and Doppler profiles ͑ based on thermal atoms ͒ , we obtained an average electron density of about (4 – 7) ϫ 10 13 cm Ϫ 3 , which is a reasonable value for the level of reduced electric field between 30 and 100 Td. However, it is well known that the theory of Stark broadening has not been properly tested for electron density below 10 14 cm Ϫ 3 . This would require an experiment that uses a spectral apparatus with an instrumental profile better than about 0.02 nm. Spectra are recorded in a wavelength range of 360–700 nm in pure hydrogen, and Ar ϩ 2.7% H 2 , and He ϩ 3% H 2 gas mixtures. The microwave excitation powers were 40 and 80 W and the gas pressure range was 0.5–10 mbar. Typical spectra recordings are shown in Fig. 4. Apart from the always present molecular hydrogen and atomic hydrogen Balmer lines, in argon and helium gas mixtures neu- tral argon and helium lines are also detected. The broad wavelength range spectra recordings did not show any indication of the excessive Balmer line broadening reported in Ref. 6. In the next step, scans of Balmer lines only are performed and typical results for H ␣ , H ␤ , and H ␥ are shown in Figs. 5 ͑ a ͒ –5 ͑ c ͒ . Again, there is no indication of excessive line broadening. For example, the FWHM of the H ␣ line ͓ see Fig. 5 ͑ a ͔͒ in pure hydrogen and in the Ar/H 2 mixture did not exceed 0.05 nm, which, if one neglects Stark and instrumental broadening, corresponds to the Doppler temperature of 1 eV. In the He/H 2 mixture the H ␣ line is broader but still smaller than 0.1 nm. Here, one should notice that the H ␣ line in the He/H 2 , and to the smaller extent in the Ar/H 2 , mixtures are self-absorbed and, if corrected for this effect, the Doppler linewidths should be smaller. These corrections are irrelevant from the point of view stated in Ref. 6, where the H ␣ linewidths equivalent to 180–210 and 110–130 eV in He/H and Ar/H mixtures, respectively, were reported. In the attempt to observe excessive Balmer line broadening in microwave-induced discharges, we measured H ␣ and H ␤ line profiles in two types of discharges, Evenson-type with a vertically polarized electric field, and the Beenakker- type with coaxially polarized electric fields. Discharges were generated in pure hydrogen or its mixture with argon or helium. The electron density in the discharges was of the order of 10 13 cm Ϫ 3 , which caused a minor Stark broadening of the observed lines. Measured line profiles had a FWHM, typically, about 0.05 nm, attributable mostly to the Stark broadening. In Ar–H 2 discharges, a limited broadening in the wings of the lines could be attributed to the presence of less than 0.01% fast hydrogen atoms with kinetic energy less than 10 eV. In spite of the uncertainties related to the nature of the observed line profiles, we can conclude that we were not able to observe the excessive Balmer line broadening seen by Mills et al. 6 Although the dynamic range of our detection systems was larger than four orders of magnitude, no large- scale effect was observed. Moreover, based on the tests related to the polarization of the electric field in a rectangular microwave cavity, we excluded the possibility of the generation of fast hydrogen atoms through a charge transfer mechanism. The work with MID in the coaxial cavity is partially supported by the Ministry of Science, Technology and De- velopment of the Republic of Serbia within Project No. ...